Conventionally, the sliding mode control has been widely applied to various systems. The sliding mode control is a variable structure type feedback control technique for previously structuring a hyperplane (a switching hyperplane) expressed by a switching function, then, converging a state variable of a controlled object on the hyperplane by a reaching law input (a reaching mode) and then, converging the state variable on a predetermined point by an equivalent control input while constraining the state variable on the hyperplane (a sliding mode). The switching function is a linear function which includes the state variable of the controlled object as a variable.
In this sliding mode control, once the state variable is converged on the hyperplane, the state variable is stably converged on a predetermined equilibrium point (converging point) on the hyperplane while the state variable is affected by the little disturbance, etc. Of course, the state variable is affected by the disturbance, etc. until the state variable is converged on the hyperplane (that is, in the reaching mode).
Conventionally, the adaptive sliding mode control has been widely applied to the various systems. The adaptive sliding mode control uses an adaptive law input (an input depending on the time integration of the switching function) in addition to the reaching law input in the normal sliding mode control in order to converge the state variable on the hyperplane. This usage of the adaptive law input substantially corresponds to the movement of the hyperplane itself. By using such an adaptive sliding mode control, the convergence of the state variable on a target value can be realized with high stability.
The sliding mode control and the adaptive sliding mode control are well known and for example, are described in detail in “SLIDING MODE CONTROL—DESIGN THEORY OF NON-LINEAR ROBUST CONTROL” attributed to KENZO NONAMI and KOKI DEN (CORONA PUBLISHING CO., LTD. 1994). Regarding the examples of the application of the adaptive sliding mode control to the control of an internal combustion engine system including a vehicle (for example, an air-fuel ratio control, an EGR control, a valve train control, a braking control, transmission control, etc.), for example, refer to the JP Examined Patent Publication No. 3261038 (the JP Unexamined Patent Publication No. 9-273440), the JP Examined Patent Publication No. 3261059 (the JP Unexamined Patent Publication No. 9-324681), the JP Examined Patent Publication No. 3819257 (the JP Unexamined Patent Publication No. 2002-364430), the JP Examined Patent Publication No. 4145520 (the JP Unexamined Patent Publication No. 2003-155938), the JP Examined Patent Publication No. 4263448 (the JP Unexamined Patent Publication No. 2004-114764), U.S. Pat. No. 5,845,491, and U.S. Pat. No. 7,813,867, etc.